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Theorem bnj1212 29269
 Description: First-order logic and set theory. (Contributed by Jonathan Ben-Naim, 3-Jun-2011.) (New usage is discouraged.)
Hypotheses
Ref Expression
bnj1212.1
bnj1212.2
Assertion
Ref Expression
bnj1212
Distinct variable group:   ,
Allowed substitution hints:   ()   ()   ()   ()   ()

Proof of Theorem bnj1212
StepHypRef Expression
1 bnj1212.1 . . 3
21bnj21 29180 . 2
3 bnj1212.2 . . 3
43simp2bi 974 . 2
52, 4bnj1213 29268 1
 Colors of variables: wff set class Syntax hints:   wi 4   wb 178   w3a 937   wceq 1653   wcel 1727  crab 2715 This theorem is referenced by:  bnj1204  29479  bnj1296  29488  bnj1415  29505  bnj1421  29509  bnj1442  29516  bnj1452  29519  bnj1489  29523 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1556  ax-5 1567  ax-17 1627  ax-9 1668  ax-8 1689  ax-6 1746  ax-7 1751  ax-11 1763  ax-12 1953  ax-ext 2423 This theorem depends on definitions:  df-bi 179  df-or 361  df-an 362  df-3an 939  df-tru 1329  df-ex 1552  df-nf 1555  df-sb 1660  df-clab 2429  df-cleq 2435  df-clel 2438  df-nfc 2567  df-rab 2720  df-in 3313  df-ss 3320
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